What is the Least Common Multiple of 34 and 50?
Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.
Least common multiple (LCM) of 34 and 50 is 850.
LCM(34,50) = 850
Least Common Multiple of 34 and 50 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34 and 50, than apply into the LCM equation.
GCF(34,50) = 2
LCM(34,50) = ( 34 × 50) / 2
LCM(34,50) = 1700 / 2
LCM(34,50) = 850
Least Common Multiple (LCM) of 34 and 50 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 34 and 50. First we will calculate the prime factors of 34 and 50.
Prime Factorization of 34
Prime factors of 34 are 2, 17. Prime factorization of 34 in exponential form is:
34 = 21 × 171
Prime Factorization of 50
Prime factors of 50 are 2, 5. Prime factorization of 50 in exponential form is:
50 = 21 × 52
Now multiplying the highest exponent prime factors to calculate the LCM of 34 and 50.
LCM(34,50) = 21 × 171 × 52
LCM(34,50) = 850